• Dec 3rd 2006, 06:20 AM
vritikagupta
1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.
• Dec 3rd 2006, 09:57 AM
CaptainBlack
Quote:

Originally Posted by vritikagupta
1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.

Every point on the path of the particle may be written:

\$\displaystyle \bold{p}=\bold{p_0}+\bold{v}t\$,

where \$\displaystyle \bold{p_0}\$ is the position of the particle at \$\displaystyle t=0\$.

Then:

\$\displaystyle \bold{p}\wedge \bold{v}= (\bold{p_0}+\bold{v}t) \wedge \bold{v}
=\bold{p_0}\wedge \bold{v}+(\bold{v} \wedge \bold{v})t=\bold{p_0}\wedge \bold{v}
\$

which is independent of \$\displaystyle t\$, and so of the particular point \$\displaystyle \bold{p}\$.

RonL